Institute of Geometry
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|Research project: Multi-parameter Persistent Homology|
This project is funded by the Austrian Science Fund (FWF) under grant P 33765-N (2021-25).
Topological data analysis is a vibrant research discipline from applied topology that combines representation theory, homological algebra, algorithms, and data analysis. Its success stems from the combination of sound mathematical theory, rich application areas and fast algorithms. The field of multi-parameter persistent homology extends the concept by analyzing data sets with several real scale parameters. The algorithmic aspects of the theory, however, have been rarely studied in the community until very recently. This is partially due to the fact that existing solutions for the single-parameter case do not extend easily to the multi-parameter case.
For multi-parameter persistence, we want to establish an algorithmic layer to facilitate the transfer from theoretical work into application areas. This includes fundamental mathematical questions, directed towards simplification and computability, the design of algorithmic solutions with provable theoretical guarantees, and the publication of software to make our findings useful in application areas.
The list of publications below also includes work performed before the runtime of the grant.